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Estimate first: a mental math trick

When to use it: Before a long calculation, and to check an answer.

Worked example

Estimating 412 × 38412 × 38 rounds to 400 × 40 = 16,000. On a line from 0, the exact 15,656 lands right beside it.412 × 38≈ 400 × 40010,00020,000estimate 16,000exact 15,656
  1. Round each number to its first digit.
  2. Do the easy calculation.
  3. Your exact answer should land near it. If it is 10 times off, a zero or a decimal point slipped.

example Round each number to its first digit, then multiply: 412 × 38

  1. 412 rounds to 400, and 38 rounds to 40.
  2. 400 × 40 = 16,000.
  3. The exact answer, 15,656, is close.

Answer: 16,000

Try three

  1. Round each number to its first digit, then multiply: 744 × 82

    Show the answer

    56,000

  2. Round each number to its first digit, then multiply: 291 × 67

    Show the answer

    21,000

  3. Round each number to its first digit, then multiply: 392 × 79

    Show the answer

    32,000

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Used in: Grouping & estimating

More mental math tricks

This technique and its worked example are Doing Math’s own lesson text, checked by a blind re-solve and a review on September 27, 2026.